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Compute the volume of a parallelpiped determined by given vectors

by RoRi

Compute the volume of the parallelpiped determined by the vectors \mathbf{i} + \mathbf{j}, \ \mathbf{j} + \mathbf{k}, \ \mathbf{k} + \mathbf{i}.

The volume is given by the scalar triple product

    \[ V = (1,1,0) \cdot (0,1,1) \times (1,0,1) = (1,1,0) \cdot (1,1,1) = 2. \]

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